Circles & Sectors: Eduqas GCSE Higher November 2018 Paper 2 Q4

Higher November 2018 Paper 2 Q4

EduqasHigherCurrent spec13 marksCircles & Sectors Percentages Properties of Numbers

4. Gregor owns a restaurant.

(a) The diagram shows a circular place mat and a square place mat.

Diagram not drawn to scale

The radius of the circular place mat is 14 cm.

(i) Calculate the circumference of the circular place mat. [2]

(ii) The area of the square place mat is 25% more than the area of the circular place mat.

Calculate the perimeter of the square place mat.
Comment on the accuracy of your answer. [6]

(b) Gregor plans to buy some spoons and forks.

A bag of 24 spoons costs £19.95.
A box of 18 forks costs £15.55.
Bags and boxes cannot be split.

Gregor decides to buy the same number of spoons as forks.
He places an order to buy the smallest number of each that he can.

Complete the details on the order form shown below.
You must show all your working. [5]

Order form with spaces for the number of bags of spoons and boxes of forks, their costs, and the total cost of the complete order

Mark scheme (a)

Scheme	Marks	Comments
(i) \((C =)\ 2 \times \pi \times 14\) or \(\pi \times 28\)	M1
Answer in the range 87.9 to 88 (cm) or \(28\pi\) (cm)	A1
(ii) (Area circle =) \(\pi \times 14^2\)	M1	(= 615(.44...) to 616 cm² or \(196\pi\))
(Area square =) \(1.25 \times \pi \times 14^2\)	M1	(= 768.75 to 770 cm² or \(245\pi\)) FT ‘their \(\pi \times 14^2\)’ provided it is dimensional correct, i.e. not for circumference
(Side of square) \(\sqrt{1.25 \times \pi \times 14^2}\)	m1	(= 27.7... cm)
(Perimeter) \(4 \times \sqrt{1.25 \times \pi \times 14^2}\)	m1	FT ‘their area of a square’ FT 4× ‘their side length’ provided at least M1 previously awarded
(Perimeter) Answer in the range 110.9 (cm) to 111 (cm)	A1	CAO
Evaluation to suit the method used, e.g. ‘rounding errors introduced by working out stage answers’, ‘it could have been worked out in one calculation without rounding errors’, ‘could be only suitable to give as a whole number’, ‘(perhaps) radius given was only accurate to nearest cm, so answer cannot be accurate to 8 decimal places’	E1

Mark scheme (b)

Scheme	Marks	Comments
\((72 \div 24 =)\) 3 (bags of spoons) AND \((72 \div 18 =)\) 4 (boxes of forks)	B3	Answers in the table take precedence over working B2 for any of the following: (least amount to buy) 72 the correct number of bags and boxes for ‘their number of common multiples’ found from making only 1 error in listing B1 for any of the following: \(24 = 6 \times 4\) and \(18 = 6 \times 3\), or similar provided the factors are broken down sufficiently to be able to find the LCM the correct number of bags and boxes for ‘their number of common multiples’ found from making 2 errors in listing
\((3 \times 19.95\) and \(4 \times 15.55 =)\) (£) 59.85 AND (£) 62.2(0)	M1	FT use of ‘their 3 bags of spoons’ and ‘their 4 boxes of forks’ provided at least B1 previously awarded
= (£) 122.05	A1	CAO
	(13)